DOCSLIB.ORG

Learning Sparse Representations in Reinforcement Learning

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Learning Sparse Representations in Reinforcement Learning Learning sparse representations in reinforcement learning Jacob Rafati, David C. Noelle Electrical Engineering and Computer Scinence Computational Cognitive Neuroscience Laboratory University of California, Merced 5200 North Lake Road, Merced, CA 95343 USA. Abstract Reinforcement learning (RL) algorithms allow artificial agents to improve their selection of ac- tions to increase rewarding experiences in their environments. Temporal Difference (TD) Learn- ing – a model-free RL method – is a leading account of the midbrain dopamine system and the basal ganglia in reinforcement learning. These algorithms typically learn a mapping from the agent’s current sensed state to a selected action (known as a policy function) via learning a value function (expected future rewards). TD Learning methods have been very successful on a broad range of control tasks, but learning can become intractably slow as the state space of the envi- ronment grows. This has motivated methods that learn internal representations of the agent’s state, effectively reducing the size of the state space and restructuring state representations in or- der to support generalization. However, TD Learning coupled with an artificial neural network, as a function approximator, has been shown to fail to learn some fairly simple control tasks, challenging this explanation of reward-based learning. We hypothesize that such failures do not arise in the brain because of the ubiquitous presence of lateral inhibition in the cortex, producing sparse distributed internal representations that support the learning of expected future reward. The sparse conjunctive representations can avoid catastrophic interference while still support- ing generalization. We provide support for this conjecture through computational simulations, demonstrating the benefits of learned sparse representations for three problematic classic control tasks: Puddle-world, Mountain-car, and Acrobot. Keywords: Reinforcement learning, Temporal Difference Learning, Learning representations, Sparse representations, Lateral inhibition, Catastrophic interference, Generalization, Midbrain Dopamine system, k-Winners-Take-All (kWTA), SARSA arXiv:1909.01575v1 [cs.LG] 4 Sep 2019 1. Introduction Reinforcement learning (RL) – a class of machine learning problems – is learning how to map situations to actions so as to maximize numerical reward signals received during the experiences that an artificial agent has as it interacts with its environment (Sutton and Barto, 1998). An RL Email addresses: [email protected] (Jacob Rafati), [email protected] (David C. Noelle) URL: http://rafati.net/ (Jacob Rafati) agent must be able to sense the state of its environment and must be able to take actions that affect the state. The agent may also be seen as having a goal (or goals) related to the state of the environment. Humans and non-human animals’ capability of learning highly complex skills by reinforcing appropriate behaviors with reward and the role of midbrain dopamine system in reward-based learning has been well described by a class of a model-free RL, called Temporal Difference (TD) Learning (Montague et al., 1996; Schultz et al., 1997). While TD Learning, by itself, certainly does not explain all observed RL phenomena, increasing evidence suggests that it is key to the brain’s adaptive nature (Dayan and Niv, 2008). One of the challenges that arise in RL in real-world problems is that the state space can be very large. This is a version of what has classically been called the curse of dimensionality. Non-linear function approximators coupled with reinforcement learning have made it possible to learn abstractions over high dimensional state spaces. Formally, this function approximator is a parameterized equation that maps from state to value, where the parameters can be construc- tively optimized based on the experiences of the agent. One common function approximator is an artificial neural network, with the parameters being the connection weights in the network. Choosing a right structure for the value function approximator, as well as a proper method for learning representations are crucial for a robust and successful learning in TD (Rafati Heravi, 2019; Rafati and Marcia, 2019; Rafati and Noelle, 2019a). Successful examples of using neural networks for RL include learning how to play the game of Backgammon at the Grand Master level (Tesauro, 1995). Also, recently, researchers at Deep- Mind Technologies used deep convolutional neural networks (CNNs) to learn how to play some ATARI games from raw video data (Mnih et al., 2015). The resulting performance on the games was frequently at or better than the human expert level. In another effort, DeepMind used deep CNNs and a Monte Carlo Tree Search algorithm that combines supervised learning and rein- forcement learning to learn how to play the game of Go at a super-human level (Silver et al., 2016). 1.1. Motivation for the research Despite these successful examples, surprisingly, some relatively simple problems for which TD coupled with a neural network function approximator has been shown to fail. For example, learning to navigate to a goal location in a simple two-dimensional space (see Figure 4) in which there are obstacles has been shown to pose a substantial challenge to TD Learning using a back- propagation neural network (Boyan and Moore, 1995). Note that the proofs of convergence to optimal performance depend on the agent maintaining a potentially highly discontinuous value function in the form of a large look-up table, so the use of a function approximator for the value function violates the assumptions of those formal analyses. Still, it seems unusual that this ap- proach to learning can succeed at some difficult tasks but fail at some fairly easy tasks. The power of TD Learning to explain biological RL is greatly reduced by this observation. If TD Learning fails at simple tasks that are well within the reach of humans and non-human animals, then it cannot be used to explain how the dopamine system supports such learning. In response to Boyan and Moore (1995), Sutton (1996) showed that a TD Learning agent can learn this task by hard-wiring the hidden layer units of the backpropagation network (used to learn the value function) to implement a fixed sparse conjunctive (coarse) code of the agent’s location. The specific encoding used was one that had been previously proposed in the CMAC model of the cerebellum (Albus, 1975). Each hidden unit would become active only when the 2 agent was in a location within a small region. For any given location, only a small fraction of the hidden units displayed non-zero activity. This is what it means for the hidden representation to be a “sparse” code. Locations that were close to each other in the environment produced more overlap in the hidden units that were active than locations that were separated by a large distance. By ensuring that most hidden units had zero activity when connection weights were changed, this approach kept changes to the value function in one location from having a broad impact on the expected future reward at distant locations. By engineering the hidden layer representation, this RL problem was solved. This is not a general solution, however. If the same approach was taken for another RL problem, it is quite possible that the CMAC representation would not be appropriate. Thus, the method proposed by Sutton (1996) does not help us understand how TD Learning might flexibly learn a variety of RL tasks. This approach requires prior knowledge of the kinds of internal representations of sensory state that are easily associated with expected future reward, and there are simple learning problems for which such prior knowledge is unavailable. We hypothesize that the key feature of the Sutton (1996) approach is that it produces a sparse conjunctive code of the sensory state. Representations of this kind need not be fixed, however, but might be learned at the hidden layers of neural networks. There is substantial evidence that sparse representations are generated in the cortex by neu- rons that release the transmitter GABA (O’Reilly and Munakata, 2001) via lateral inhibition. Biologically inspired models of the brain show that, the sparse representation in the hippocam- pus can minimize the overlap of representations assigned to different cortical patterns. This leads to pattern separation, avoiding the catastrophic interference, but also supports generalization by modifying the synaptic connections so that these representations can later participate jointly in pattern completion (O’Reilly and McClelland, 1994; Noelle, 2008). Computational cognitive neuroscience models have shown that a combination of feedfor- ward and feedback inhibition naturally produces sparse conjunctive codes over a collection of excitatory neurons (O’Reilly and Munakata, 2001). Such patterns of lateral inhibition are ubiq- uitous in the mammalian cortex (Kandel et al., 2012). Importantly, neural networks containing such lateral inhibition can still learn to represent input information in different ways for different tasks, retaining flexibility while producing the kind of sparse conjunctive codes that may support reinforcement learning. Sparse distributed representation schemes have the useful properties of coarse codes while reducing the likelihood of interference between different representations. 1.2. Objective of the paper In this paper, we demonstrate how incorporating a ubiquitous feature of biological neural networks into the artificial neural
Load more

Recommended publications
  • Backpropagation and Deep Learning in the Brain
    Backpropagation and Deep Learning in the Brain Simons Institute -- Computational Theories of the Brain 2018 Timothy Lillicrap DeepMind, UCL With: Sergey Bartunov, Adam Santoro, Jordan Guerguiev, Blake Richards, Luke Marris, Daniel Cownden, Colin Akerman, Douglas Tweed, Geoffrey Hinton The “credit assignment” problem The solution in artificial networks: backprop Credit assignment by backprop works well in practice and shows up in virtually all of the state-of-the-art supervised, unsupervised, and reinforcement learning algorithms. Why Isn’t Backprop “Biologically Plausible”? Why Isn’t Backprop “Biologically Plausible”? Neuroscience Evidence for Backprop in the Brain? A spectrum of credit assignment algorithms: A spectrum of credit assignment algorithms: A spectrum of credit assignment algorithms: How to convince a neuroscientist that the cortex is learning via [something like] backprop - To convince a machine learning researcher, an appeal to variance in gradient estimates might be enough. - But this is rarely enough to convince a neuroscientist. - So what lines of argument help? How to convince a neuroscientist that the cortex is learning via [something like] backprop - What do I mean by “something like backprop”?: - That learning is achieved across multiple layers by sending information from neurons closer to the output back to “earlier” layers to help compute their synaptic updates. How to convince a neuroscientist that the cortex is learning via [something like] backprop 1. Feedback connections in cortex are ubiquitous and modify the
    [Show full text]
  • Training Autoencoders by Alternating Minimization
    Under review as a conference paper at ICLR 2018 TRAINING AUTOENCODERS BY ALTERNATING MINI- MIZATION Anonymous authors Paper under double-blind review ABSTRACT We present DANTE, a novel method for training neural networks, in particular autoencoders, using the alternating minimization principle. DANTE provides a distinct perspective in lieu of traditional gradient-based backpropagation techniques commonly used to train deep networks. It utilizes an adaptation of quasi-convex optimization techniques to cast autoencoder training as a bi-quasi-convex optimiza- tion problem. We show that for autoencoder configurations with both differentiable (e.g. sigmoid) and non-differentiable (e.g. ReLU) activation functions, we can perform the alternations very effectively. DANTE effortlessly extends to networks with multiple hidden layers and varying network configurations. In experiments on standard datasets, autoencoders trained using the proposed method were found to be very promising and competitive to traditional backpropagation techniques, both in terms of quality of solution, as well as training speed. 1 INTRODUCTION For much of the recent march of deep learning, gradient-based backpropagation methods, e.g. Stochastic Gradient Descent (SGD) and its variants, have been the mainstay of practitioners. The use of these methods, especially on vast amounts of data, has led to unprecedented progress in several areas of artificial intelligence. On one hand, the intense focus on these techniques has led to an intimate understanding of hardware requirements and code optimizations needed to execute these routines on large datasets in a scalable manner. Today, myriad off-the-shelf and highly optimized packages exist that can churn reasonably large datasets on GPU architectures with relatively mild human involvement and little bootstrap effort.
    [Show full text]
  • Q-Learning in Continuous State and Action Spaces
    -Learning in Continuous Q State and Action Spaces Chris Gaskett, David Wettergreen, and Alexander Zelinsky Robotic Systems Laboratory Department of Systems Engineering Research School of Information Sciences and Engineering The Australian National University Canberra, ACT 0200 Australia [cg dsw alex]@syseng.anu.edu.au j j Abstract. -learning can be used to learn a control policy that max- imises a scalarQ reward through interaction with the environment. - learning is commonly applied to problems with discrete states and ac-Q tions. We describe a method suitable for control tasks which require con- tinuous actions, in response to continuous states. The system consists of a neural network coupled with a novel interpolator. Simulation results are presented for a non-holonomic control task. Advantage Learning, a variation of -learning, is shown enhance learning speed and reliability for this task.Q 1 Introduction Reinforcement learning systems learn by trial-and-error which actions are most valuable in which situations (states) [1]. Feedback is provided in the form of a scalar reward signal which may be delayed. The reward signal is defined in relation to the task to be achieved; reward is given when the system is successfully achieving the task. The value is updated incrementally with experience and is defined as a discounted sum of expected future reward. The learning systems choice of actions in response to states is called its policy. Reinforcement learning lies between the extremes of supervised learning, where the policy is taught by an expert, and unsupervised learning, where no feedback is given and the task is to find structure in data.
    [Show full text]
  • Double Backpropagation for Training Autoencoders Against Adversarial Attack
    1 Double Backpropagation for Training Autoencoders against Adversarial Attack Chengjin Sun, Sizhe Chen, and Xiaolin Huang, Senior Member, IEEE Abstract—Deep learning, as widely known, is vulnerable to adversarial samples. This paper focuses on the adversarial attack on autoencoders. Safety of the autoencoders (AEs) is important because they are widely used as a compression scheme for data storage and transmission, however, the current autoencoders are easily attacked, i.e., one can slightly modify an input but has totally different codes. The vulnerability is rooted the sensitivity of the autoencoders and to enhance the robustness, we propose to adopt double backpropagation (DBP) to secure autoencoder such as VAE and DRAW. We restrict the gradient from the reconstruction image to the original one so that the autoencoder is not sensitive to trivial perturbation produced by the adversarial attack. After smoothing the gradient by DBP, we further smooth the label by Gaussian Mixture Model (GMM), aiming for accurate and robust classification. We demonstrate in MNIST, CelebA, SVHN that our method leads to a robust autoencoder resistant to attack and a robust classifier able for image transition and immune to adversarial attack if combined with GMM. Index Terms—double backpropagation, autoencoder, network robustness, GMM. F 1 INTRODUCTION N the past few years, deep neural networks have been feature [9], [10], [11], [12], [13], or network structure [3], [14], I greatly developed and successfully used in a vast of fields, [15]. such as pattern recognition, intelligent robots, automatic Adversarial attack and its defense are revolving around a control, medicine [1]. Despite the great success, researchers small ∆x and a big resulting difference between f(x + ∆x) have found the vulnerability of deep neural networks to and f(x).
    [Show full text]
  • Unsupervised Speech Representation Learning Using Wavenet Autoencoders Jan Chorowski, Ron J
    1 Unsupervised speech representation learning using WaveNet autoencoders Jan Chorowski, Ron J. Weiss, Samy Bengio, Aaron¨ van den Oord Abstract—We consider the task of unsupervised extraction speaker gender and identity, from phonetic content, properties of meaningful latent representations of speech by applying which are consistent with internal representations learned autoencoding neural networks to speech waveforms. The goal by speech recognizers [13], [14]. Such representations are is to learn a representation able to capture high level semantic content from the signal, e.g. phoneme identities, while being desired in several tasks, such as low resource automatic speech invariant to confounding low level details in the signal such as recognition (ASR), where only a small amount of labeled the underlying pitch contour or background noise. Since the training data is available. In such scenario, limited amounts learned representation is tuned to contain only phonetic content, of data may be sufficient to learn an acoustic model on the we resort to using a high capacity WaveNet decoder to infer representation discovered without supervision, but insufficient information discarded by the encoder from previous samples. Moreover, the behavior of autoencoder models depends on the to learn the acoustic model and a data representation in a fully kind of constraint that is applied to the latent representation. supervised manner [15], [16]. We compare three variants: a simple dimensionality reduction We focus on representations learned with autoencoders bottleneck, a Gaussian Variational Autoencoder (VAE), and a applied to raw waveforms and spectrogram features and discrete Vector Quantized VAE (VQ-VAE). We analyze the quality investigate the quality of learned representations on LibriSpeech of learned representations in terms of speaker independence, the ability to predict phonetic content, and the ability to accurately re- [17].
    [Show full text]
  • Approaching Hanabi with Q-Learning and Evolutionary Algorithm
    St. Cloud State University theRepository at St. Cloud State Culminating Projects in Computer Science and Department of Computer Science and Information Technology Information Technology 12-2020 Approaching Hanabi with Q-Learning and Evolutionary Algorithm Joseph Palmersten [email protected] Follow this and additional works at: https://repository.stcloudstate.edu/csit_etds Part of the Computer Sciences Commons Recommended Citation Palmersten, Joseph, "Approaching Hanabi with Q-Learning and Evolutionary Algorithm" (2020). Culminating Projects in Computer Science and Information Technology. 34. https://repository.stcloudstate.edu/csit_etds/34 This Starred Paper is brought to you for free and open access by the Department of Computer Science and Information Technology at theRepository at St. Cloud State. It has been accepted for inclusion in Culminating Projects in Computer Science and Information Technology by an authorized administrator of theRepository at St. Cloud State. For more information, please contact [email protected]. Approaching Hanabi with Q-Learning and Evolutionary Algorithm by Joseph A Palmersten A Starred Paper Submitted to the Graduate Faculty of St. Cloud State University In Partial Fulfillment of the Requirements for the Degree of Master of Science in Computer Science December, 2020 Starred Paper Committee: Bryant Julstrom, Chairperson Donald Hamnes Jie Meichsner 2 Abstract Hanabi is a cooperative card game with hidden information that requires cooperation and communication between the players. For a machine learning agent to be successful at the Hanabi, it will have to learn how to communicate and infer information from the communication of other players. To approach the problem of Hanabi the machine learning methods of Q- learning and Evolutionary algorithm are proposed as potential solutions.
    [Show full text]
  • Linear Prediction-Based Wavenet Speech Synthesis
    LP-WaveNet: Linear Prediction-based WaveNet Speech Synthesis Min-Jae Hwang Frank Soong Eunwoo Song Search Solution Microsoft Naver Corporation Seongnam, South Korea Beijing, China Seongnam, South Korea [email protected] [email protected] [email protected] Xi Wang Hyeonjoo Kang Hong-Goo Kang Microsoft Yonsei University Yonsei University Beijing, China Seoul, South Korea Seoul, South Korea [email protected] [email protected] [email protected] Abstract—We propose a linear prediction (LP)-based wave- than the speech signal, the training and generation processes form generation method via WaveNet vocoding framework. A become more efficient. WaveNet-based neural vocoder has significantly improved the However, the synthesized speech is likely to be unnatural quality of parametric text-to-speech (TTS) systems. However, it is challenging to effectively train the neural vocoder when the target when the prediction errors in estimating the excitation are database contains massive amount of acoustical information propagated through the LP synthesis process. As the effect such as prosody, style or expressiveness. As a solution, the of LP synthesis is not considered in the training process, the approaches that only generate the vocal source component by synthesis output is vulnerable to the variation of LP synthesis a neural vocoder have been proposed. However, they tend to filter. generate synthetic noise because the vocal source component is independently handled without considering the entire speech To alleviate this problem, we propose an LP-WaveNet, production process; where it is inevitable to come up with a which enables to jointly train the complicated interactions mismatch between vocal source and vocal tract filter.
    [Show full text]
  • Lecture 11 Recurrent Neural Networks I CMSC 35246: Deep Learning
    Lecture 11 Recurrent Neural Networks I CMSC 35246: Deep Learning Shubhendu Trivedi & Risi Kondor University of Chicago May 01, 2017 Lecture 11 Recurrent Neural Networks I CMSC 35246 Introduction Sequence Learning with Neural Networks Lecture 11 Recurrent Neural Networks I CMSC 35246 Some Sequence Tasks Figure credit: Andrej Karpathy Lecture 11 Recurrent Neural Networks I CMSC 35246 MLPs only accept an input of fixed dimensionality and map it to an output of fixed dimensionality Great e.g.: Inputs - Images, Output - Categories Bad e.g.: Inputs - Text in one language, Output - Text in another language MLPs treat every example independently. How is this problematic? Need to re-learn the rules of language from scratch each time Another example: Classify events after a fixed number of frames in a movie Need to resuse knowledge about the previous events to help in classifying the current. Problems with MLPs for Sequence Tasks The "API" is too limited. Lecture 11 Recurrent Neural Networks I CMSC 35246 Great e.g.: Inputs - Images, Output - Categories Bad e.g.: Inputs - Text in one language, Output - Text in another language MLPs treat every example independently. How is this problematic? Need to re-learn the rules of language from scratch each time Another example: Classify events after a fixed number of frames in a movie Need to resuse knowledge about the previous events to help in classifying the current. Problems with MLPs for Sequence Tasks The "API" is too limited. MLPs only accept an input of fixed dimensionality and map it to an output of fixed dimensionality Lecture 11 Recurrent Neural Networks I CMSC 35246 Bad e.g.: Inputs - Text in one language, Output - Text in another language MLPs treat every example independently.
    [Show full text]
  • A Guide to Recurrent Neural Networks and Backpropagation
    A guide to recurrent neural networks and backpropagation Mikael Bod´en¤ [email protected] School of Information Science, Computer and Electrical Engineering Halmstad University. November 13, 2001 Abstract This paper provides guidance to some of the concepts surrounding recurrent neural networks. Contrary to feedforward networks, recurrent networks can be sensitive, and be adapted to past inputs. Backpropagation learning is described for feedforward networks, adapted to suit our (probabilistic) modeling needs, and extended to cover recurrent net- works. The aim of this brief paper is to set the scene for applying and understanding recurrent neural networks. 1 Introduction It is well known that conventional feedforward neural networks can be used to approximate any spatially finite function given a (potentially very large) set of hidden nodes. That is, for functions which have a fixed input space there is always a way of encoding these functions as neural networks. For a two-layered network, the mapping consists of two steps, y(t) = G(F (x(t))): (1) We can use automatic learning techniques such as backpropagation to find the weights of the network (G and F ) if sufficient samples from the function is available. Recurrent neural networks are fundamentally different from feedforward architectures in the sense that they not only operate on an input space but also on an internal state space – a trace of what already has been processed by the network. This is equivalent to an Iterated Function System (IFS; see (Barnsley, 1993) for a general introduction to IFSs; (Kolen, 1994) for a neural network perspective) or a Dynamical System (DS; see e.g.
    [Show full text]
  • Feedforward Neural Networks and Word Embeddings
    Feedforward Neural Networks and Word Embeddings Fabienne Braune1 1LMU Munich May 14th, 2017 Fabienne Braune (CIS) Feedforward Neural Networks and Word Embeddings May 14th, 2017 · 1 Outline 1 Linear models 2 Limitations of linear models 3 Neural networks 4 A neural language model 5 Word embeddings Fabienne Braune (CIS) Feedforward Neural Networks and Word Embeddings May 14th, 2017 · 2 Linear Models Fabienne Braune (CIS) Feedforward Neural Networks and Word Embeddings May 14th, 2017 · 3 Binary Classification with Linear Models Example: the seminar at < time > 4 pm will Classification task: Do we have an < time > tag in the current position? Word Lemma LexCat Case SemCat Tag the the Art low seminar seminar Noun low at at Prep low stime 4 4 Digit low pm pm Other low timeid will will Verb low Fabienne Braune (CIS) Feedforward Neural Networks and Word Embeddings May 14th, 2017 · 4 Feature Vector Encode context into feature vector: 1 bias term 1 2 -3 lemma the 1 3 -3 lemma giraffe 0 ... ... ... 102 -2 lemma seminar 1 103 -2 lemma giraffe 0 ... ... ... 202 -1 lemma at 1 203 -1 lemma giraffe 0 ... ... ... 302 +1 lemma 4 1 303 +1 lemma giraffe 0 ... ... ... Fabienne Braune (CIS) Feedforward Neural Networks and Word Embeddings May 14th, 2017 · 5 Dot product with (initial) weight vector 2 3 2 3 x0 = 1 w0 = 1:00 6 x = 1 7 6 w = 0:01 7 6 1 7 6 1 7 6 x = 0 7 6 w = 0:01 7 6 2 7 6 2 7 6 ··· 7 6 ··· 7 6 7 6 7 6x = 17 6x = 0:017 6 101 7 6 101 7 6 7 6 7 6x102 = 07 6x102 = 0:017 T 6 7 6 7 h(X )= X · Θ X = 6 ··· 7 Θ = 6 ··· 7 6 7 6 7 6x201 = 17 6x201 = 0:017 6 7
    [Show full text]
  • Long Short-Term Memory 1 Introduction
    LONG SHORTTERM MEMORY Neural Computation J urgen Schmidhuber Sepp Ho chreiter IDSIA Fakultat f ur Informatik Corso Elvezia Technische Universitat M unchen Lugano Switzerland M unchen Germany juergenidsiach ho chreitinformatiktumuenchende httpwwwidsiachjuergen httpwwwinformatiktumuenchendehochreit Abstract Learning to store information over extended time intervals via recurrent backpropagation takes a very long time mostly due to insucient decaying error back ow We briey review Ho chreiters analysis of this problem then address it by introducing a novel ecient gradientbased metho d called Long ShortTerm Memory LSTM Truncating the gradient where this do es not do harm LSTM can learn to bridge minimal time lags in excess of discrete time steps by enforcing constant error ow through constant error carrousels within sp ecial units Multiplicative gate units learn to op en and close access to the constant error ow LSTM is lo cal in space and time its computational complexity p er time step and weight is O Our exp eriments with articial data involve lo cal distributed realvalued and noisy pattern representations In comparisons with RTRL BPTT Recurrent CascadeCorrelation Elman nets and Neural Sequence Chunking LSTM leads to many more successful runs and learns much faster LSTM also solves complex articial long time lag tasks that have never b een solved by previous recurrent network algorithms INTRODUCTION Recurrent networks can in principle use their feedback connections to store representations of recent input events in form of activations
    [Show full text]
  • Boosted Backpropagation Learning for Training Deep Modular Networks
    Boosted Backpropagation Learning for Training Deep Modular Networks Alexander Grubb [email protected] J. Andrew Bagnell [email protected] School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213 USA Abstract tor which is itself a network of simpler modules. Ap- proaches leveraging such modular networks have been Divide-and-conquer is key to building sophis- successfully applied to real-world problems like natural ticated learning machines: hard problems are language processing (NLP) (Lawrence et al., 2000; Ro- solved by composing a network of modules hde, 2002), optical character recognition (OCR) (Le- that solve simpler problems (LeCun et al., Cun et al., 1998; Hinton et al., 2006), and robotics 1998; Rohde, 2002; Bradley, 2009). Many (Bradley, 2009; Zucker et al., 2010). Figure1 shows such existing systems rely on learning algo- an example network for a robotic autonomy system rithms which are based on simple paramet- where imitation learning is used for feedback. ric gradient descent where the parametriza- tion must be predetermined, or more spe- These deep networks are typically composed of layers cialized per-application algorithms which are of learning modules with multiple inputs and outputs usually ad-hoc and complicated. We present along with various transforming modules, e.g. the acti- a novel approach for training generic mod- vation functions typically found in neural network lit- ular networks that uses two existing tech- erature, with the end goal of globally optimizing net- niques: the error propagation strategy of work behavior to perform a given task. These con- backpropagation and more recent research on structions offer a number of advantages over single descent in spaces of functions (Mason et al., learning modules, such as the ability to compactly rep- 1999; Scholkopf & Smola, 2001).
    [Show full text]